Show that any positive odd integer is of the form 6q + 1 or 6q + 3 or 6q + 5 where qz
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hey
here is answer
let a be any positive integer
then
b=5
0≤r<b
0≤r<6
r=0,1,2, 3,4, 5
case 1.
r=0
a=bq+r
6q+0
6q
case 2.
r=1
a=bq+r
6q+1
case 3.
r=2
6q+2
case4.
r=3
6q+3
case 5.
r=4
6q+4
case 6
r=5
6q+5
from above it is proved.
hope it helps
thanks
here is answer
let a be any positive integer
then
b=5
0≤r<b
0≤r<6
r=0,1,2, 3,4, 5
case 1.
r=0
a=bq+r
6q+0
6q
case 2.
r=1
a=bq+r
6q+1
case 3.
r=2
6q+2
case4.
r=3
6q+3
case 5.
r=4
6q+4
case 6
r=5
6q+5
from above it is proved.
hope it helps
thanks
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